Question

. The rectangle has a perimeter of 28 cm and a diagonal length of 10 cm. Determine the dimensions of the rectangle.

Answer 1

Good morning ☕️

Answer:

Length = 8 cm

width = 6 cm

Step-by-step explanation:

consider L the length of the rectangle and w its width.

Statement 1 : The rectangle has a perimeter of 28

means  L + w = 14

statement 2 : the rectangle has a diagonal length of 10

means  10² = L² + w²

we obtain :

L = 14 - w           (1)

100 = L² + w²    (2)

if we substitute L by 14 - w in equation (2) we get:

100 = (14 - w)² + w² ⇔ w² - 14w + 98 = 0

solve the quadratic equation and you’ll get:

w = 6 or w = 8

now back to equation (1)

L = 14 - w = 14 - 6 = 8

then w = 6 and L = 8

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Answer 2

Answer: length = 8cm; width = 6cm

Step-by-step explanation:

The dimensions of a rectangle are the length and width:

Let x be the length of rectangle, and

y, the width of rectangle

Perimeter equals 2x+2y=28, divide through by 2: x+y=14

Make y the subject, y=14-x, input the value of y into the equation and solve by pythagorean theorem:

x^2 + y^2= 10^2 = 100

x^2 + (14-x)^2 =100

x^2 +196-28x + x^2= 100

2x^2- 28x +196= 100

2x^2 -28x +96 =0

x^2 -14x + 48= 0

(x- 8) (x- 6)= 0

x= 8; or x = 6

The length of rectangle is 8 cm

The width of rectangle is 6 cm

I hope this helps.