Question

the area of a rectangle is 300 cm square and its length: breadth= 4:3. find its perimeter and the length of its diagonal.

Answer 1

Area =l×b
Ratio=4:3
then 4a×3a=300
12a^2=300
a^2=300/12
a^2=25
a=5
then l=4a=4×5=20
b=3a=3×5=15
Perimeter=2(l+b)
P=2(20+15)
P=70
Diagonal=25

Answer 2

The perimeter is 70 cm and the length of diagonal is 25 cm

Step-by-step explanation:

We are given that the ratio length to breadth is 4:3

So, Length = 4x

Breadth =3x

Area of rectangle = $Length \times Breadth = 4x \times 3x = 12x^2$

We are given that the area of a rectangle is 300 cm square

So, $12x^2 = 300 \\x=\sqrt{\frac{300}{12}}$

x=5

Length = 4x =4(5)=20 cm

Breadth =3x=3(5)=15 cm

Perimeter of rectangle =2(l+b)=2(20+15)=70 cm

Length of diagonal = $\sqrt{l^2+b^2}$

Length of diagonal =$\sqrt{20^2+15^2}$

Length of diagonal =25 cm

Hence The perimeter is 70 cm and the length of diagonal is 25 cm

#Learn more:

The length and the breadth of a rectangle are 16 cm and 12 cm respectively. Find

(1) its perimeter, (2) the length of its diagonal, 3) its area

(b) If the area of a rectangle is 63 cm and its breadth is 7 cm. find its) length and perimeter

(c) The perimeter of a rectangle is 40 cm and the ratio of its length and breadth is 3:2. Find

(1) the length of its diagonal, and (2) its area.

(d) The area of a rectangle is 300 cm and its length: breadth = 4:3. Find (i) its perimeter and

(ii) the length of its diagonal.​

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