Equation maths Num xxx 08/07/2023 A right triangle has a maximum area of 450 square inches. Find the length of the perimeter.
Fey Garcia 08/07/2023 at 3:50 am Max area of rightΔ A=h²/4 => h= hypothenuse 450=h²/4 h=30√2 in. Find a & b A=1/2ab ab=2A 900=ab a=900/b c²=a²+b² (30√2)²=a²+(a/900)² a=30 b=30 => a=b P=30√2 +30+30 P=60√2 +2 P≈102.43 Reply
Viswanadhan VS 08/07/2023 at 3:50 am As the right triangle has maximum area it must be an isosceles right triangle. Area = 1/2 a^2 450=1/2 a^2 a^2=900 a=30 Hypotenuse=√(a^2+a^2) = √(1800) =30√2 Therefore, perimeter =30+30+30√2 =30(2+√2) square inches Reply
30(2+√2)
Max area of rightΔ
A=h²/4
=> h= hypothenuse
450=h²/4
h=30√2 in.
Find a & b
A=1/2ab
ab=2A
900=ab
a=900/b
c²=a²+b²
(30√2)²=a²+(a/900)²
a=30
b=30
=> a=b
P=30√2 +30+30
P=60√2 +2
P≈102.43
30(2+sqrt2)in
30(1+sqrt2)in ?
{450÷π}^2×2×π
As the right triangle has maximum area it must be an isosceles right triangle.
Area = 1/2 a^2
450=1/2 a^2
a^2=900
a=30
Hypotenuse=√(a^2+a^2)
= √(1800)
=30√2
Therefore, perimeter =30+30+30√2
=30(2+√2) square inches