The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?

Question

The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side? (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/chemistry/8256cc2f7381e3ce31700b1c2432d8a0-.png" /> Sides a - d , a , a + d AP ( a + d )2= a 2+( a - d )2 ⇒ a =4 d Area =24 (1/2) a(a-d) =24 a(a-d) =48 12 d2 =48 d =2 (d > 0) ∴ a =8 So, sides 6, 8, 10

Q. The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$ , then what is the length of its smallest side?

Sides $a - d, a, a + d A P$
$(a + d)^{2} = a^{2} + (a - d)^{2}$
$\Rightarrow a = 4 d$
Area $= 24$
$\frac{1}{2} a (a - d) = 24$
$a (a - d) = 48$
$12 d^{2} = 48$
$d = 2 (d > 0)$
$∴ a = 8$
So, sides $6, 8, 10$

Q. The sides of a right angled triangle are in arithmetic progression. If the triangle has area 24, then what is the length of its smallest side?

Sides a−d,a,a+dAP (a+d)2=a2+(a−d)2 ⇒a=4d Area =24 21​a(a−d)=24 a(a−d)=48 12d2=48 d=2(d>0) ∴a=8 So, sides 6,8,10

Q. The sides of a right angled triangle are in arithmetic progression. If the triangle has area $24$ , then what is the length of its smallest side?

Sides $a - d, a, a + d A P$
$(a + d)^{2} = a^{2} + (a - d)^{2}$
$\Rightarrow a = 4 d$
Area $= 24$
$\frac{1}{2} a (a - d) = 24$
$a (a - d) = 48$
$12 d^{2} = 48$
$d = 2 (d > 0)$
$∴ a = 8$
So, sides $6, 8, 10$