Question

(ii) In the figure, ZABC = 90°, AB = 3x, BC = 4x and AC = 30, then
А A
30
3x
C
B
4x
(a) Using Pythagoras theorem, determine the value of x.
(b) Find the length of segments AB and BC.
(c) Find A (AABC).​

Answer 1

Answer:

We are given that in △ABC,∠=90

tyhe sides of △ABC is given by

AB=x cm,BC=(4x+4)cm &

AC=(4x+5) cm

From the pythagoras theorem,

AC 2=AB

2+BC2

So,

(4x+5) 2 −(x) 2 +(4x+4) 216x 2+40x+25=x 2 +16x+22z−16

∴ 16x

2

+40x+25=17x

2

+32x+16

∴ x

2

−8x−9=0

∴ (x−9)(x+1)=0

∴ x=9 or x=−1

but distance cannot be negative

So, x=9

Now, sides are AB=x=9 cm

BC=4(9)+4=40 cm

AC=4(9)+5=41 cm

Step-by-step explanation:

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