Problem 1: 071206
Square In A Triangle
1. The figure shows a square inscribe in a triangle, right angled at B. If AP = 8 cm, SC = 12 cm, find, in cm2, the area of the square.
2. If AP = x, SC = y, find, in terms of x and y, the area of the square.
3. Construct a triangle ABC right angled at B. Show how to inscribe a square PQRS As shown above.
6 comments:
This is a question that 99 out of 100 university students may answer wrongly: One day, a man went to Mr Wong's shop to buy a gift. The cost(成本)of the gift was RM 18 while its selling price was RM 21. This man paid Mr Wong a RM 100 note but Mr Wong didn't have small change so he changed the RM 100 note into small change with the shopkeeper of the shop next to him and gave a change of RM 79 to the man. Later, the shopkeeper of the shop next to him discovered that the RM 100 note is a fake(伪造) one. So, Mr Wong was forced to replace the RM 100 note with another one.
Question:
What is the loss of Mr Wong in this sale?
这是一题100位大学生有99位答错的IQ题…
一天，有个年轻人到王老板的店里买一件礼物。这件礼物的成本是18元，标价是21元，结果这年轻人掏出100元要买这件礼物。
王老板当时没有零钱，用那零钱向街坊换了100元的零钱，找给年轻人79元，但是街坊后来发现那100是假的，王老板无奈还了街坊100元。
现在的问题是：王老板在这次的交易中到底损失了多少钱?
Dear teacher,
Where should I submit my solutions?
(a)
64 + x² +144 + x² = 400
x² = 192 / 2 = 96
x = 9.798 cm
Area of square = x²
= 9.798 x 9.798 = 96 cm²
(b)
a = side of square , a² = area
a²+ x² + a²+ y² = (x+y) ²
2a² + x² + y² = ( x+y) ²
2a² + ( x+y) ² - 2xy = ( x+y) ²
2a² = 2xy
a² = xy
Area = xy
angle QBR,RSC & QPA right angle
angle SRC = angle BQR = angle QAP
angle BRQ = angle RCS = angle AQP
therefore triangle QAP,BQR & RSC similar
we get RS : SC
AP : QP
RS : 12
8 : QP
RS*QP = 12*8
RS=QP
RS sq = 96
Area of PQRS = RS sq = 96 cm sq
angle QBR,RSC & QPA right angle
angle SRC = angle BQR = angle QAP
angle BRQ = angle RCS = angle AQP
therefore triangle QAP,BQR & RSC similar
we get RS : y
x : QP
RS=QP
RS: y
x :RS
Therefore,Area of PQRS is xy
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