The length and breadth of a rectangle are in the ratio 4:3 and the diagonal measures 10 cm. It's perimeter is
Answers
Answer:
28 cm
Step-by-step explanation:
This is quite simple.
To start, we are given that the length and breadth of a rectangle are in the ratio 4:3. We can take the constant magnitude as x.
Hence, we can say :
Length of the rectangle - 4x
Breadth of the rectangle - 3x
Hence, Perimeter (of a rectangle) = 2 (4x + 3x)
= 14x.
We are also given that the diagonal measures 10 cm.
Hence, that diagonal divides the rectangle into two triangles with the uncommon sides of the triangles being the length and breadth of the rectangle.
Through the Pythagorean theorem, we know :
a^2 + b^2 = c^2.
The diagonal = c (as it is the hypotenuse).
So, the two sides (length and breadth) of the rectangle are designated to the values a and b. Substituting,
(4x)^2 + (3x)^2 = (10)^2
= 25x^2 = 100 cm [Transpose 25 to RHS]
x^2 = 4 cm
Hence, x (rational magnitude) = 2 cm.
Recall that the perimeter = 14x = 14(2 cm) = 28 cm.
That's your answer!