Question

perimeter of a rectangle is 42 cm . If diagonal is 15 cm find the breadth

Answer 1

Answer:

Step-by-step explanation:

p=2(l+b)

42=2(15+b)

42=30+2b

2b=12

b=6

Answer 2

Given:

The perimeter of a rectangle=42 cm

Diagonal=15 cm

To find:

The breadth of the rectangle

Solution:

The breadth of the rectangle is 9 or 12.

We can find the breadth by following the given steps-

We are given that the length of the diagonal is 15cm.

In a rectangle, the length of the diagonal can be obtained using the Pythagoras theorem.

Since each angle of a rectangle is 90°, the diagonal, length and breadth form a right-angled triangle.

Let the length of the rectangle be L and the breadth be B.

Using Pythagoras theorem,

$Diagonal^{2} =Length^{2} +Breadth^{2}$

$15^{2}$=$L^{2} +B^{2}$

225=$L^{2} +B^{2}$ (1)

Now, the perimeter of the rectangle=2(Length +Breadth)

=2(L+B)

We are given that the perimeter is 42 cm.

So, 42=2(L+B)

21=L+B (2)

Squaring both sides,

$21^{2}$=$(L+B)^{2}$

441=$L^{2} +B^{2}$+2LB

From (1),

441=225+2LB

441-225=2LB

216=2LB

108=LB

108/B=L

Substituting the value of L in (2),

21=108/B+B

21B=108+$B^{2}$

We will solve the quadratic equation by using the factorization method.

$B^{2}$-21B+108=0

$B^{2}$-12B-9B+108=0

B(B-12)-9(B-12)=0

(B-9)(B-12)=0

Now either B-9=0 or B-12=0

So, B=9 or 12

Therefore, the breadth of the rectangle is 9 or 12.