Question

A carpenter is framing a wall that is 8 feet high and 15 feet long. If the carpenter wants to be sure that the sides of the wall meet at right angles, then what should the diagonal measurement of the wall be?

Answer 1

If you cut the rectangle (the wall) diagonally, you get two congruent triangles. The measurements of the sides of one the triangles is 8, 15 and x. There is a pythagorean triples 8, 15, 17 so x has to be 17. if you dont know the triple you can do a^2 + b^2 = c^2         8^2 + 15^2 = c^2     c = 17

the diagonal of wall should be 17

Answer 2

Answer:

17 feet.

Step-by-step explanation:

Let x represent the length of diagonal of wall.

We have been given that a carpenter is framing a wall that is 8 feet high and 15 feet long. The carpenter wants to be sure that the sides of the wall meet at right angles.

Since sides of wall meet at right triangle, so length, height and diagonal of wall will form a right triangle and diagonal will be hypotenuse of right triangle.

We will Pythagoras theorem to solve for diagonal as:

$\text{Leg}^2+\text{Leg}^2=\text{Hypotenuse}^2$

$8^2+15^2=x^2$

$64+225=x^2$

$289=x^2$

Switch sides:

$x^2=289$

Take square root of both sides:

$\sqrt{x^2}=\pm \sqrt{289}$

$x=\pm 17$

Since length cannot be negative, therefore, the measurement of diagonal should be 17 feet.