Answer:
P = 28 cm
Step-by-step explanation:
the diagonal divides the rectangle into 2 right triangles with the diagonal as hypotenuse.
the ratio of length : breadth = 4 : 3 = 4x : 3x ( x is a multiplier )
using Pythagoras' identity in the right triangle
(4x)² + (3x)² = 10²
16x² + 9x² = 100
25x² = 100 ( divide both sides by 25 )
x² = 4 ( take square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
then
length = 4x = 4 × 2 = 8 cm
breadth = 3x = 3 × 2 = 6 cm
perimeter (P) is calculated as
P = 2 × length + 2 × breadth
= 2 × 8 + 2 × 6
= 16 + 12
= 28 cm
Answer:
perimeter = 28 cm
Step-by-step explanation:
[tex]\frac{L}{w} =\frac{4}{3}[/tex]
Then
[tex]L = \frac{4}{3} w[/tex]
By applying the Pythagorean theorem:
L² + w² = 10²
Then
[tex]\left( \frac{4}{3} w\right)^{2} +w^{2}=100[/tex]
Then
[tex]\frac{16}{9} w^{2} +w^{2}=100[/tex]
Then
[tex]\frac{25}{9} w^{2}=100[/tex]
Then
[tex]w^2=\frac{9\times100}{25} =\frac{900}{25}[/tex]
Then
w = 30/5
= 6
Then
[tex]L = \frac{4}{3} \times6 = \frac{24}{3} =8[/tex]
Perimeter = 2×(L + w)
= 2×(8 + 6)
= 2×(14)
= 28
