Question

PQR is a right angled triangle in which PQ = QR. If the hypotenuse of the triangle is 20 cm, then what is the area (in cm2) of the triangle PQR?

Answer 1

$\textbf{\underline{\underline{Answer:}}}$

In the figure above QR is base, PQ is perpendicular to QR and PR is hypotenuse.

$\textbf{\underline{\underline{Given\:that}}}$

Length of PR = 20 cm (Hypotenuse)

PQ = QR

Using Pythagoras Theorem :

< (Hypotenuse)^2 = (Perpendicular)^2 + (Base)^2

< (20)^2 = (PQ)^2 + (QR)^2

[ We can take 2 PQ as both are equal]

< 400 = 2(PQ)^2

< (PQ)^2 = 400/2

< (PQ)^2 = 200

< (PQ) = √200

< PQ = 10√2

[ PQ = QR = 10√2 cm ]

$\textbf{\underline{\underline{Area\:Of\:Triangle\:PQR}}}$

We know that Area of Triangle =

◆ 1/2 × Base × Height

[ Here, Base = 10√2 cm and Height =10√2 cm ]

◆ 1/2 × 10√2 × 10√2

◆ 100cm^2

Answer 2

$\huge{ANSWER}$

The area of ∠PQR = 50cm².

ꜱᴛᴇᴩ-ʙy-ꜱᴛᴇᴩ ᴇxᴩʟᴀɴᴀᴛɪᴏɴ :

$Given \ that :$

PQR is a right angled triangle.
PQ = QR.
The hypotenuse of the triangle is 20 cm.
To Find :

The area of the triangle PQR? (in cm²).

$๏ℓµţɨ๏ɲ ⤵

ɪᴛ ɪꜱ ɢɪᴠᴇɴ ᴛʜᴀᴛ ᴩQʀ ɪꜱ ᴀ ʀɪɢʜᴛ ᴀɴɢʟᴇᴅ ᴛʀɪᴀɴɢʟᴇ. ꜱᴏ, ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ ᴛʜᴇʀᴇ ɪꜱ ᴛʜᴇᴏʀᴍ ꜰᴏʀ ʀɪɢʜᴛ ᴀɴɢʟᴇᴅ ꜰɪɢᴜʀᴇꜱ ᴄᴀʟʟᴇᴅ "ᴩyᴛʜᴀɢᴏʀᴀꜱ ᴛʜᴇᴏʀᴍ."

We know :

• P² + B² => H²

Values in Equation,

=> (20)² = 2(pq)²
=> 400² = 2(pq)²
=> 2(pq)² = 400
=> 2(pq) = √400
=> 2(pq) = 20
=> PQ = 10
=> QR = 10

==> Area =
$\frac{1}{2} \times b \times h \\ \\ \frac{1}{2} \times 10 \times 10 \\ \\ = = > {50cm}^{2}$
rєffєr tσ αttαchmєnt σf fígurє.

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