Question

find AB if the area of the triangle ABC is 48m² and the height CD is 12 m​

Answer 1

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• Area of ∆ABC = 48m² and height CD is 12m.

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}$

• Base AB

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• Area of ∆ABC = 48m²

• Height CD = 12m

• Base AB = ?

We know that,

$\boxed{\pink{\sf Area \: of \: triangle \: = \: \dfrac{1}{2} \: * \: h \: * \: b}}$

Substituting the values,

• $\sf Area \: of \: \triangle ABC \: = \: \dfrac{1}{2} \: * \: CD \: * \: AB$

• $\sf 48 \: = \: \dfrac{1}{2} \: * \: 12 \: * \: AB$

• $\sf 48 \: = \: \dfrac{1}{2} \: * \: 12 \: * \: AB$

• $\sf 48 \: = \: \dfrac{1}{\cancel{2}} \: * \: \cancel{12} \: * \: AB$

• $\sf 48 \: = \: 6 \: * \: AB$

• $\sf \dfrac{48}{6} \: = \: AB$

• $\sf \dfrac{\cancel{48}}{\cancel{6}} \: = \: AB$

• $\sf AB \: = \: 8m$

Therefore,

• $\underline{\boxed{\therefore{\purple{\tt{Base \: AB \: = \: 8m}}}}}$

Answer 2

Answer:

• 8 m

Step-by-step explanation:

Given

• Area of the ΔABC = 48 m²
• Height CD = 12 m

To find

• Base AB = ? m

Solution

⇾ Area of triangle = 1/2 × Base × Height

⇾ Area of ΔABC = AB × CD

⇾ 48 = 1/2 × AB × 12

⇾ 48 = AB × 6

⇾ AB = 48/6

⇾ AB = 8

∴ Base AB of the Δ ABC is 8 m.

Verification

⇾ Area of triangle = 1/2 × Base × Height

⇾ 48 = 1/2 × 8 × 12

⇾ 48 = 4 × 12

⇾ 48 = 48

⇾ L.H.S = R.H.S