The hypotenuse of a right triangle is 8 more than the shorter leg. The longer leg is 4 more than the shorter l?
Let's call the length of the short leg "x." (I'm introducing a variable for it because it's what we want to find out.) > The hypotenuse of a right triangle is 8 more than the shorter leg. Then the hypotenuse has length x + 8. > The longer leg is 4 more than the shorter leg. Then the longer leg has length x + 4. Since we're talking about a right triangle, then the Pythagorean Theorem applies, so we know: x^2 + (x + 4)^2 = (x + 8)^2. Expanding out what's in the parentheses gives x^2 + x^2 + 8x + 16 = x^2 + 16x + 64 This is a quadratic equation, so to solve it, we can collect everything on one side and factor. Subtracting x^2 from each side gives x^2 + 8x + 16 = 16x + 64 Subtracting 16x gives x^2 - 8x + 16 = 64 Subtracting 64 gives x^2 - 8x - 48 = 0 The left side factors: (x - 12)(x + 4) = 0 Two things multiply to make zero just when one of the factors is itself zero, so this means x - 12 = 0 or x + 4 = 0 which is the same as x = 12 or x = -4. The solution x = -4 doesn't make sense in the context of the problem, because x measures the length of the side of a triangle. So the length of the shorter leg must be 12.
He shorter leg of a right triangle is 5 meters. The hypotenuse is 1 meter longer than the longer leg. Find the length of the longer leg.?
You can work this out using Pythagoras theorem - a^2+b^2=c^2 So: 5^2+b^2=(b+1)^2 25+b^2=b^2+1 25-1=2b^2 14=2b^2 7=b^2 Therefore the answer is that b equals the square root of 7
The hypotenuse of a right triangle is 26 feet long. one leg is 14 feet longer than the other. find the length?
Given: c = 26 ft, hypotenuse of a top triangle a = x, length of one leg b = x + 14, length of the different leg discover: lengths of the legs answer: using the Pythagorean Theorem: c^2 = a^2 + b^2 (26)^2 = x^2 + (x + 14)^2 676 = x^2 + x^2 + 28x + 196 x^2 + x^2 + 28x + 196 = 676 2x^2 + 28x + 196 - 676 = 0 2x^2 + 28x - 480 = 0 Divide by using 2 the two left and top of the equations.... x^2 + 14x - 240 = 0 Factoring: (x + 24)(x - 10) = 0 Equate each and every binomial ingredient to 0.... x + 24 = 0 x = -24 ignore this answer because of the fact it rather is unfavourable. x - 10 = 0 x = 10 ANS the different leg is, x + 14 = 10 + 14 = 24 ANS teddyboy
The shorter leg of a right triangle is 5 meters. The hypotenuse is 1 meter longer than the longer leg. Find the length of the longer leg.?
crnio has the right answer...I got the same thing from the same process. From 2nd to 3rd step seems unclear though. From here: 25 + x² = x² + 2x + 1 Subtract x² from both sides. 25 = 2x + 1 And then subtract 1 from both sides. 25 = 2x And then divide both sides by 2. And you're left with the answer. x = 12. So the length of the longer leg is 12 meters. The length of the hypotenuse is 13 meters. This makes sense because we know that 5, 12, & 13 are Pythagorean triples, or a set of numbers that we know will satisfy the Pythagorean theorem. As a refresher, the theorem is, when you have a right triangle (that is a triangle with a 90 degree angle), you can this relationship between the side lengths to figure out how long they are: a² +b² = c² Where a & b are legs, and c is the hypotenuse. This can all be a little confusing, but only at first. If you have any questions you can click on my name, go to my profile and email me and I'll do my best to help.
One leg of a right triangle is 2 meters longer than the other leg. the hypotenuse is 2 meters less than twice?
Ok, so the formula for the right triangle is: h^2 = a^2 + b^2 where h = hypotenuse, a = shorter leg and b = longer leg with the conditions given, a = a (need to find) b = a+2 h = 2a-2 substituting h^2 = a^2 + b^2 (2a-2)^2 = a^2 + (a+2)^2 4a^2 - 8a + 4 = a^2 + a^2 + 4a + 4 4a^2 - 8a + 4 = 2a^2 + 4a + 4, simplifying 4a^2 - 8a + 4 - 2a^2 - 4a - 4 = 0 2a^2 - 12a = 0 2a(a - 6) = 0 (dividing both equation by 2a) a - 6 = 0 Therefore, a = 6 meters Proving, a = a = 6 b = a+2 = 8 h = 2a-2 = 10 h^2 = a^2 + b^2 10^2 = 6^2 + 8^2 100 = 36 + 64 100 = 100 QED!
The hypotenuse of a right triangle is 25m long. the length of one leg is 10m less than twice the other.?
let c=hypotenuse a,b = legs therefore: c=25 a=2b-10 form pythagorean theorem; a^2+b^2 = c^2 (2b - 10)^2 + b^2 = 25^2 4b^2 - 40b + 100 + b^2 = 625 5b^2 - 40b - 525 = 0 dividing both sides by 5 b^2 - 8b - 105 = 0 factoring the left side (b - 15)(b + 7) = 0 b + 7 = 0 b = -7 absurd (no side can be negative) b - 15 = 0 b = 15 solve for a: a = 2b - 10 a = 2*15 - 10 a = 20 therefor the two legs of the right triangle are 20 cm and 15 cm checking: c^2 = 20^2 + 15^2 c^2 = 400 + 225 c^2 = 625 c = 25 cm. that's it
One leg of a right triangle is 5 cm shorter than the other leg.?
The formula for right triangles, with the two legs being a and b, and the hypotenuse being c, is: a^2 + b^2 = c^2 So we have a as the shortest leg, b = (a + 5) as the longer leg, and then c = 25, so: a^2 + (a + 5)^2 = 25^2, with a being the length of the shorter leg. Now expand: a^2 + (a^2 + 10a + 25) = 625 2a^2 + 10a + 25 = 625 pull all to one side: 2a^2 + 10a - 600 = 0 divide by 2 a^2 + 5a - 300 = 0 factor: (a + 20) * (a - 15) = 0 so, a + 20 = 0 a - 15 = 0 a = -20 or 15 Since the side of a triangle cannot have a negative length, the -20 is disregarded, and we are left with: The shorter leg has length 15 cm.
The Pythagorean Theorem states that [math] a^2 + b^2 = c^2 [/math], where a and b are the legs, and c is the hypotenuse. We can use this with the problem at hand, plugging in 5 as the hypotenuse and 2 as the leg: [math] 2^2 + b^2 = 5^2 \rightarrow 4+b^2=25 \rightarrow b^2=21 \rightarrow b=\fbox{\sqrt{21}}[/math].REMEMBER: the Pythagorean Theorem is extremely useful. You will use it countless times in problems, as well as to prove various concepts in more advanced mathematics.
Find the length of the shorter leg of a right triangle if the longer leg is 24 meters..?
short leg = x hypotenuse=2x+6 use the pythagorean theorem x^2+24^2=(2x+6)^2 ; distribute x^2+576=4x^2+12x+12x+36 ; combine like terms x^2+576=4x^2+24x+36 ; subtract x^2 and 576 0=3x^2+24x-540 ; divide by 3 0=x^2+8x-180 ; factor 0=(x+18)(x-10) ; x can equal -18 or 10 so the shorter leg = 10
NOTE: IT IS MAXIMUM SURFACE AREA THAT IS ASKED FOR,NOT VOLUME !We have to Rotate an ISOCELES right-angle △ of maximum area,about its hypotenuse to generate two cones base-to-base of MAXIMUM SURFACE AREA=2(πrl)=2π(5)(5√2)=(50√2)π in²≈222.144 in²●■★WORKINGS:h=hypotenuse of right-angle △r=radius of cone=½h=½×10=5x=equal side of GIVEN right-angle △h²=x²+x²=2x² 【Pythagoras Theorem】x²=½h²=½×10²=100/2=50x=√50=5√2l=slant height of generated cone=x=5√2