Question

The perimeter of a rectangle is 28 cm and its diagonal is 10 cm.
a) What is the sum of its width and height ?
b) If the width is taken as 7+x. then the height=--------c) What are the length of its sides? ​

Answer 1

Step-by-step explanation:

Given perimeter = 28cm.

2(x + y) = 28

x + y = 14

y = 14 - x -------- (1)

Now,

By Pythagoras s theorem.

x^2 + y^2 = 10^2

x^2 + y^2 = 100

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

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

2x^2 - 28x + 196 = 100

2x^2 - 28x + 196 - 100 = 0

2x^2 - 28x + 96 = 0

x^2 - 14x + 48 = 0

x^2 - 6x - 8x + 48 = 0

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

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

x = 6,8

y = 14 - 6, 14 - 8

= 8,6

Therefore the length = 8cm, breadth = 6cm.

Area of the rectangle = length * breadth

= 8 * 6

= 48cm^2.

Hope this helps!

Answer 2

Answer:

Step-by-step explanation:

Perimeter of a rectangle is  = 2(width + height)

                                              = 2(w + h)

                                              = 28

So w + h = 14..........(1)

(a) Sum of width and height = 14 cm

diagonal is 10 cm, so according to Pythagoras theorem

w² + h² = 10² = 100..........(2)

From equation (1) and (2) only two solution are possible

w = 8, h = 6 or w = 6, h = 8

(b) If the width is taken as 7+x, it means width is 8 cm

     And height is 6cm

(c) Width = 8 cm

    Height = 6 cm