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Answer:
Nᴜᴍʙᴇʀ 1 is explained below ☟︎︎︎
The diagonal ACAC has length 2424cm.
AEAE is half of ACAC, so the length is 1212cm.
ABEABE is a right triangle with sides AB=15AB=15cm and AE=12AE=12cm.
Using the Pythagorean Theorem, BE=9BE=9cm.
Diagonal BDBD is twice the length of BEBE, therefore it is 1818cm.
Using the area formula A=d1d22A=d1d22, we have 18×242=2162
Number 2 is 117.15cm2
Number 3 is explained below ☟︎︎︎
Equating Eq. 2 & 3: 482−(25+x)2=252−x2482−(25+x)2=252−x2
Expanding this:482−252−50x−x2=252−x2482−252−50x−x2=252−x2
⇒50x=482−2×252⇒50x=482−2×252
⇒x=482−2×25250=2304−125050=105450=21.08⇒x=482−2×25250=2304−125050=105450=21.08
Let’s feed this value of xx into Eq. 2
h2=482−(25+x)2=2304−46.082=2304−2123.3664=180.6336h2=482−(25+x)2=2304−46.082=2304−2123.3664=180.6336
⇒h=180.6336−−−−−−−√=13.44⇒h=180.6336=13.44
Feeding this value into Eq. 1: Area=25×13.44=336Area=25×13.44=336
Answer: 336 sq. cm
number 3 = Answer: 336 sq. cm
Number 4 is explained below ☟︎︎︎
Area of a rhombus = 240 sq cm = d1*d2/2, or
if d1 = 11 cm, then d2 = 2*240/8 = 60 cm.
The other diagonal = 60 cm.
Method 2: Area of rhombus = 240 cm.
Area of each triangle = 240/2 =120 sq cm.
If the base of the triangle = 08 cm, the altitude of the triangle =120*2/08 = 30 cm.
The other diagonal = 2 * altitude of the triangle = 2*30 = 60 cm.
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