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german
3 years ago
5

The shorter leg of a right triangle is 7 centimeters nbspless than the other leg. Find the length of the two legs if the hypoten

use is 13 centimeter

Mathematics
1 answer:
AlladinOne [14]3 years ago
4 0

Answer:

The shorter leg of the right triangle is 5\ cm

The other leg of the right triangle is 12\ cm

Step-by-step explanation:

Let

x-----> the shorter leg of a right triangle

y----> the larger leg of a right triangle

we know that

Applying the Pythagoras Theorem

13^{2}=x^{2} +y^{2} ----> equation A

x=y-7 ----> equation B

substitute equation B in equation A and solve for y

13^{2}=(y-7)^{2} +y^{2}\\169=y^{2} -14y+49+y^{2} \\2y^{2}-14y-120=0

using a graphing tool----> solve the quadratic equation

The solution is y=12\ cm

see the attached figure

Find the value of x

x=12-7=5\ cm

therefore

The shorter leg of the right triangle is 5\ cm

The other leg of the right triangle is 12\ cm

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