In △abc, point d∈ac with ad: dc=4: 3, point e∈bc so that be: ec=1: 5. if acde=5 in2, find abdc, aabd, and aabc.

A diagram can be helpful.

When triangles have the same altitude, their areas are proportional to their base lengths.

The altitude from D to line BC is the same for triangles BDC and EDC. The base lengths of these triangles have the ratio ...

... BC : EC = (1+5) : 5 = 6 : 5

so ABDC will be 6/5 times AEDC.

... ABDC = (6/5)×(5 in²)

... ABDC = 6 in²

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The altitude from B to line AC is the same for triangles BDC and BDA, so their areas are proportional to their base lengths. That is ...

... AABD : ABDC = AD : DC = 4 : 3

so AABD will be 4/3 times ABDC.

... AABD = (4/3)×(6 in²)

... AABD = 8 in²

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Of course, AABC is the sum of the areas of the triangles that make it up:

... AABC = AABD + ABDC = 8 in² + 6 in²

... AABC = 14 in²

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: