Question

An architect wants to draw a rectangle with a diagonal of 25 centimeters. The length of the rectangle is to be 10 centimeters more than twice the width. What dimensions should she make the rectangle?

Answer 1

The dimensions she would take are length = 24cm and width = 7cm

What is a rectangle?

A rectangle is a polygon with 4 sides and 4 right angles.

Analysis:

let the width be = x

Length = 2x + 10

Diagonal = 25

The diagonal, length and width of the rectangle form a right angle triangle and by Pythagoras,

$(25)^{2}$ = $x^{2}$ + $(2x + 10)^{2}$

625 = $x^{2}$ + 4$x^{2}$ + 40x + 100

5$x^{2}$ + 40x +100 - 625 = 0

5 $x^{2}$ + 40x - 525 = 0

divide through by 5

$x^{2}$ + 8x - 105 = 0

$x^{2}$ +15x - 7x - 105

x(x + 15) -7(x + 15) = 0

(x-7)(x+15) = 0

since dimension cannot be negative x = 7

so width is 7cm

Length = 2x+ 10 = 2(7) + 10 = 24cm

In conclusion, the dimensions are 24cm and 7cm.

Learn more about rectangles: brainly.com/question/25292087

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