The length of a rectangle is 24 cm and its
diagonal is 30 cm. Find its breadth and area.
(118
Ton
Answers
Answer:
The value of breadth is 18 cm
The value of Area is 432 cm²
Step-by-step explanation:
use Pythagoras theorem,
(length)² + (breadth)² = (diagonal)²
(24)² + (breadth)² = (30)²
(breadth)² = 900 -576
(breadth)² = 324
breadth = √324
breadth = 18
Now area of rectangle = length x breadth
Area of rectangle = 24 x 18
= 432 cm²
Given :-
- Shape = Rectangle
- Length of the rectangle = 24cm
- Diagonal of the Rectangle = 30cm
To Find :-
- It's Breadth and Area .
Solution :-
➞ Diagonal = √(Length)² + (Breadth)²
➞ 30 = √(24)² + (Breadth)²
➞ (30)² = (24)² + (Breadth)²
➞ 30 × 30 = 24 × 24 + (Breadth)²
➞ 900 = 576 + (Breadth)²
➞ 900 - 576 = (Breadth)²
➞ 324 = (Breadth)²
➞ √324 = Breadth
➞ 18cm = Breadth
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➞ Area of Rectangle = Length × Breadth
➞ Area of Rectangle = 24 × 18
➞ Area of Rectangle = 432cm²
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Therefore, Area of the Rectangle is 432cm² and Breadth of the Rectangle is 18cm
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★ Additional Info :
Formulas Related to Rectangle :
- Perimeter of Rectangle = 2( l + b)
- Area = Length × Breadth
- Length = Area / Breadth
- Breadth = Area / Length
- Diagonal = √(l)² + (b)²
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