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3 years ago

Solve for a and b. please help.

Mathematics

1 answer:

Pachacha [2.7K]3 years ago

3 0

Answer:

a= 22.5

b= 37.5

Step-by-step explanation:

In △BCD:

Applying Pythagoras' Theorem,

a² +30²= b²

a² +900= b² -----(1)

In △ABC:

Applying Pythagoras' Theorem,

b² +50²= (40 +a)² -----(2)

Substitute (1) into (2):

a² +900 +50²= 40² +2(40)(a) +a² (expand bracket)

a² +900 +2500= 1600 +80a +a²

a² +3400= a² +80a +1600 (simplify)

a² +3400 -a² -80a -1600= 0 (bring everything to 1 side)

-80a +1800= 0

80a= 1800 (+80 on both sides)

a= 1800 ÷80

a= 22.5

Subst. a= 22.5 into (1):

22.5² +900= b²

b²= 506.25 +900

b²= 1406.25

b= √1406.25 (square root both sides)

b= 37.5 (reject negative value since b is a length)

☆(a +b)²= a² +2ab +b²

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