Question

Calculate the length of side BC


If the area of triangle CBD is 120 cm2, Calculate the area of triangle ABE.

The scale factor is 4. (Please answer separately it's two different questions and it's a test!)

Answer 1

Step-by-step explanation:

Clearly, the triangle BCD and triangle ABE are similar.

$\frac{bc}{be} = \frac{bd}{ab} \\ \frac{bc}{8} = \frac{5}{10} \\ bc = 4$

hope it helps you

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Answer 2

$question$

ΔABC is right angled at A. AD is perpendicular to BC. If AB=5cm, BC=13cm and AC=12cm, find the area of ΔABC. Also, find the length of AD.

Solution

In right angles triangle BAC, AB=5cm and AC=12

$area \: of \: triangle \: = \frac{1}{2} \times base \times height \times \frac{1}{2} \times ab \times ac \\ = \frac{1}{2} \times 5 \times 12 = 30cm {}^{2}$

Now, in ΔABC,

$area \: of \: triangle \: abc \: = \frac{1}{2} \times bc \times ad \\ => 30 = \frac{1}{2} \times 13 \times ad \\ => ad \: = \frac{30 \times 2}{13} = \frac{60}{30}$