The length of a rectangle is the square root of 65 cm the diagonal of the rectangle is 5 cm more than the width find in centimeters the width of a rectangle

Question

I can’t do this because my teacher never taught me how to do diagonals so how does she expect me to do one with a square root that can’t be simplified. Also tell me how you did it.

Answer 1

The diagonal of the rectangle forms TWO right triangles

Length = sqrt(65)

width is w

Hypotenuse is (w+5)

Pythagorean theorem says [ sqrt(65)]^2 + w^2 = (w+5)^2

65 + w^2 = w^2 + 10w + 25

65 = 10w + 25

40 = 10w

w = 4

width is 4

length is sqrt(65)

Square of the Hypotenuse is 4^2 + sqrt(65)^2 = 16 + 65 = 81 = 9^ = (4+5)^2 = (w+5)^2

Answer 2

Stephen, draw a picture.

l = √65

hypotenuse = w + 5

w^2 + (w + 5)^2 = √65 ^2

w^2 + (w + 5)^2 = 65

w^2 + w^2 + 10w + 25 = 65

2w^2 + 10w -40 = 0

w^2 + 5w - 20 = 0

w = 2.62

I used the quadratic