Question

ICERT)
OT garden = 16 meter.
Q.9. The area of a right angled triangle is 30 cm². If its
height is 7 cm more than its length of base, then
find the length of its base.
12019)
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Answer 1

Answer:

The length of its base = 5 cm

Step-by-step explanation:

Given:

The area of a right-angled triangle = 30 cm².

Let the length of its base x cm.

Length of height = (x + 7) cm.

Formula: Area of a right-angled triangle = (½ × b × h) sq. units

According to question:

½ × x × (x + 7) = 30

→ x² + 7x = 60

→ x² + 7x - 60 = 0

→ x² + 12x - 5x - 60 = 0

→ x(x + 12) - 5(x + 12) = 0

→ (x - 5) (x + 12) = 0

→ x = 5 or x = - 12

But length always taken postive: i.e., x = 5

∴ Base = x = 5 cm

∴ Height = x + 7 = 5 + 7 = 12 cm

Answer 2

$\; \; \; \; \; \; \; \; \;{\Large{\bf{\underbrace{Required \; answer}}}}$

${\large{\bold{\rm{\underline{Question}}}}}$

✠ The area of a right angled triangle is 30 cm². If its height is 7 cm more than its length of base, then find the length of its base.

${\large{\bold{\rm{\underline{Given \; that}}}}}$

✰ The area of right angled triangle is 30 cm²

✰ The height of that right angled triangle is 7 cm more than its length of base.

${\large{\bold{\rm{\underline{To \; find}}}}}$

✰ The length of right angled triangle's base.

${\large{\bold{\rm{\underline{Solution}}}}}$

✰ The length of right angled triangle's base = 12 cm

${\large{\bold{\rm{\underline{Assumptions}}}}}$

✰ a is the length of ∆ base

✰ Length of height is (7+a) because it's more than the length of it's base.

${\large{\bold{\rm{\underline{Using \; concept}}}}}$

✰ Formula to find area of triangle

${\large{\bold{\rm{\underline{Using \; formula}}}}}$

✰ A of triangle = ½ × B × H

${\large{\bold{\rm{\underline{Where,}}}}}$

⋆ B denotes base

⋆ H denotes height

⋆ A denotes area

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

⇢ A of triangle = ½ × B × H

⇢ 30 = ½ × a × (7+a)

⇢ 60 = a × (7+a)

⇢ b × h = 60

Formed equation,

⇢ a × (7+a) = 60 (Equation 1)

Now, let's carry on

⇢ 7a + a² = 60

⇢ a² + 7a - 60 = 0

⇢ a² + 12a - 5a - 60 = 0

⇢ a(a+12) - 5(a+12) = 0

⇢ (a-5) (a+12) = 0

⇢ a = -5 or 12

⇢ a = 5 or -12

Note - We can't take length in negative so,

★ 5 cm measures base (a) here

★ Height =

⇢ a + 7

⇢ 5 + 7

⇢ 12 cm